---
title: On the densest MIMO lattices from cyclic division algebras
url: https://www.emergentmind.com/papers/0703052
type: paper
arxiv_id: '0703052'
arxiv_url: https://arxiv.org/abs/0703052
published: '2007-03-12'
categories:
- cs.IT
- math.IT
---

# On the densest MIMO lattices from cyclic division algebras

## Abstract

It is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant. Using results from class field theory a lower bound to the minimum discriminant of a maximal order with a given center and index (= the number of Tx/Rx antennas) is derived. Also numerous examples of division algebras achieving our bound are given. E.g. we construct a matrix lattice with QAM coefficients that has 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant. We describe a general algorithm due to Ivanyos and Ronyai for finding maximal orders within a cyclic division algebra and discuss our enhancements to this algorithm. We also consider general methods for finding cyclic division algebras of a prescribed index achieving our lower bound.